If my condo unit was damaged by two shared common elements (pipes) and the home owners' association opened two claims on the master policy with a $10,000 deductible each, who pays the deductible?

My layman's view. Party A suffered damage because of stuff done by Party B. Party B pays. The fact that PartyB has full insurance / no insurance / partial insurance only affects whether they CAN, not whether they SHOULD.

The Association probably could have left you to your own insurance--since the damage is to your unit--but it has proceeded as if they are liable by submitting a claim to theirs. As a matter of first impression then, their insurance, their deductible, they pay. The wrinkle of course, is if their insurer actually agrees that it is liable and actually pays benefits. It's very possible their insurer might refuse to pay benefits arguing that they insured against damage, which occurred in your unit and not in the insured common element. It may not be over yet.This answer is not a substitute for professional legal advice....